You can keep some girls for your own use, no problem.Can you beat the game without prostitution/sharing any girl? Looking for a challenge.
Getting Sena and Lena's approval will require you to prostitute at least one woman. Getting that approval within standard run of 50 days might require more than one prostitute. It's hard to tell how reputation works. But filling one of every kind of room would certainly be enough. If I were you, I would restrict myself to one glory hole room in the brothel and see if it is possible.
You can have any girl outside of brothel have only one unique partner, although the typical strategy is super-incest where a single woman is the partner of her son, grandson, grand-grandson and so on. But you don't really need to do that, if you're willing to dedicate two breeding pairs (with supporting infrastructure) to any monster sale goal you're getting.